In this work, we present a nonparametric Bayesian method for multivariate volatility modeling. Our approach is based on postulation of a novel mixture of multioutput heteroscedastic Gaussian processes to model the covariance matrices of multiple assets. Specifically, we use the Pitman-Yor process prior as the nonparametric prior imposed over the components of our model, which are taken as multioutput heteroscedastic Gaussian processes obtained by introducing appropriate convolution kernels that combine simple heteroscedastic Gaussian processes under a multioutput scheme. We exhibit the efficacy of our approach in a volatility prediction task.